The Colin De Verdière Graph Parameter for Threshold Graphs
نویسنده
چکیده
We consider Schrödinger operators on threshold graphs and give an explicit construction of a Colin de Verdière matrix for each connected threshold graph G of n vertices. We conclude the Colin de Verdière graph parameter μ(G) satisfies μ(G) ≥ n− i− 1, where i is the number of isolates in the graph building sequence. The proof is algorithmic in nature, constructing a particular Colin de Verdiére matrix M . As a corollary to the construction, we give estimates on the size of the non-zero eigenvalues of M .
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تاریخ انتشار 2006